Systems of Linear Inequalities Quiz 1 Review

Systems of Linear Inequalities Quiz 1 Review

Graphing a Linear Inequality

• Ensure the inequality is written in slope-intercept form. This may flip the sign!

• Graph a line using the slope and y-intercept.

  • Use a solid line if the inequality includes "or equal to"

  • Use a dotted line if the inequality does not include "or equal to"​

• Shade above or below the line

  • Above if the inequality symbol is "greater than"

  • Below if the inequality symbol is "less than"​

​2. Graph the line with the y-intercept being 1 and the slope being -1/3. Use a solid line since the inequality symbol includes "or equal to".

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3. Shade below the line since the inequality symbol is "less than"​

 

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​2. Graph the line with the y-intercept being -2 and the slope being 1/2. Use a dotted line since the inequality symbol does not include "or equal to".

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3. Shade above the line since the inequality symbol is "less than"​

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NOTE! When solving for y, we divided by a negative, and this changed the direction of our sign!​

 

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Graphing a System of Linear Inequalities

• Ensure both inequalities are written in slope-intercept form. This may flip the sign!

• Graph both of the inequalities in the same graph.

  • Graph a line using the slope and y-intercept.

    • Use a solid line if the inequality includes "or equal to"

    • Use a dotted line if the inequality does not include "or equal to"​

  • Shade above or below the line

    • Above if the inequality symbol is "greater than"

    • Below if the inequality symbol is "less than"​​

• The region where the shading overlaps is the solution set to the system of inequalities.

Multiple Choice

This graph represents the solution set to which inequality?

• $$2x+5y>5$$  

• $$2x-5y<5$$  

• $$5x+2y>-2$$  

• $$5x-2y<2$$  

Multiple Choice

This graph represents the solution set to which inequality?

• $$4x+y\ge2$$  

• $$x+4y\le8$$  

• $$4x-y\ge-2$$  

• $$x-4y\le-8$$  

Multiple Choice

Select the graph that represents the solution set to the system of inequalities shown.

Multiple Choice

Select the graph that represents the solution set to the system of inequalities shown.

Multiple Choice

Which of the following ordered pairs is in the solution set of the given inequality?

• (10,5)

• (-5,10)

• (10,-5)

• (5,10)

Multiple Choice

Select the graph that represents the solution set to the system of inequalities shown.

Multiple Choice

Which of the following ordered pairs is in the solution set of the given inequality?

• (5,0)

• (-2,0)

• (0,-2)

• (0,5)